This assignment is for ETC5521 Assignment 2 based on Team emu comprising of Justin Thomas and Mayunk Bharadwaj. and revised by Abhishek Sinha and Yiwen Zhang.
Using the data provided on the ‘tidytuesday’ platform, our primary question is to identify the characteristics of a winning beach volleyball team for both males and females.
We believe that there might be differences in characteristics for a winning team compared to a losing team because of, for example, prevalence of beach volleyball in certain countries. Also, we theorize that taller and younger players may potentially be better at beach volleyball because of the competitive advantage they may have over shorter and more seasoned players.
Therefore, the secondary questions that will help us answer our primary question are:
Furthermore, We will further explore the individual qualities of individual players in the team to identify the most successful player and the most successful combination. In addition to the physiological quality (height, age) and technical factors, we will also study whether the winning team will be affected by the home advantage.
After studying the characteristics of the winning team, we will also be very curious about an interesting question. Although the winning team is likely to be a strong team (high ranking ), is there any situation that the low ranking team defeats the high ranking team? So, we add four additional questions to complete this analysis:
In the following report, the reader will be able to find a description and information about the source and limitations of the data; information on how the data was cleaned; an analysis that will answer the above questions and a conclusion.
While going through the dataset, we found that the data was incomplete because there were multiple ‘NA’ values for individual player performance statistics. As such, observations which featured ‘NA’ values had to be removed as they were unlikely to be helpful in our analysis. Due to this, the sample size will be reduced, which means that the accuracy of the research results may be affected to a certain extent.
Primary Question
What are the characteristics of a winning beach volleyball team for both males and females?
Secondary Questions
Additional Questions for Assignment 2
Looking into the FVIB circuit, is there any home advantage for winning players?
Is there any low ranking team beat higher ranking team?
What combination of the players are most successful and have teamed up for the greatest number of matches in both the volleyball circuits?
Who are the most successful players in beach volleyball and how they have evolved over time and their skills pattern?
This data set provides beach volleyball statistics for men’s and women’s matches at two major tournaments, the Fédération Internationale de Volleyball (FIVB) Beach Volleyball World Championships and the Association of Volleyball Professionals (AVP) tour. The matches are played with teams of 2. In this data set, tournament information, player information, player performance statistics and match results are recorded. The data provided ranges from September 2000 to August 2019 and it has been collected by the data recorded at the tournaments.
The original data source created by Adam Vagner had initial data recorded from September 2000 to July 2017, however it has been periodically updated with the most recent update coming in May 2020. This can be found at this website on Github.(BigTimeStats, n.d.)
The structure of the data set is:
There are 65 variables in this data set:
| Variable Name |
|---|
| circuit |
| tournament |
| country |
| year |
| date |
| gender |
| match_num |
| w_player1 |
| w_p1_birthdate |
| w_p1_age |
| w_p1_hgt |
| w_p1_country |
| w_player2 |
| w_p2_birthdate |
| w_p2_age |
| w_p2_hgt |
| w_p2_country |
| w_rank |
| l_player1 |
| l_p1_birthdate |
| l_p1_age |
| l_p1_hgt |
| l_p1_country |
| l_player2 |
| l_p2_birthdate |
| l_p2_age |
| l_p2_hgt |
| l_p2_country |
| l_rank |
| score |
| duration |
| bracket |
| round |
| w_p1_tot_attacks |
| w_p1_tot_kills |
| w_p1_tot_errors |
| w_p1_tot_hitpct |
| w_p1_tot_aces |
| w_p1_tot_serve_errors |
| w_p1_tot_blocks |
| w_p1_tot_digs |
| w_p2_tot_attacks |
| w_p2_tot_kills |
| w_p2_tot_errors |
| w_p2_tot_hitpct |
| w_p2_tot_aces |
| w_p2_tot_serve_errors |
| w_p2_tot_blocks |
| w_p2_tot_digs |
| l_p1_tot_attacks |
| l_p1_tot_kills |
| l_p1_tot_errors |
| l_p1_tot_hitpct |
| l_p1_tot_aces |
| l_p1_tot_serve_errors |
| l_p1_tot_blocks |
| l_p1_tot_digs |
| l_p2_tot_attacks |
| l_p2_tot_kills |
| l_p2_tot_errors |
| l_p2_tot_hitpct |
| l_p2_tot_aces |
| l_p2_tot_serve_errors |
| l_p2_tot_blocks |
| l_p2_tot_digs |
Our data was already in tidy format, so we did not have much cleaning to do. However in order to conduct our analysis, we have tidied the data set by removing variables that are not pertinent to answer our questions or include too many missing values.
The methods we have used to tidy our data is as follows:
The reason for why we did not include variables such as match duration, or some individual player performance statistics was because it did not fit with answering the first three questions we have laid out. Additionally, majority of the data for these variables were unknown, so it would not have been enough in our additional analysis.
| Variable | Description |
|---|---|
| circuit | Either AVP (USA) or FIVB (International) |
| country | Country where tournament played |
| year | Year of tournament |
| date | Date of match |
| gender | Gender of team |
| w_player1 | Winner player 1 Name |
| w_p1_age | Winner player 1 age |
| w_p1_hgt | Winner player 1 height in inches |
| w_p1_country | Winner player country |
| w_player2 | Winner player 2 name |
| w_p2_age | Winner player 2 age |
| w_p2_hgt | Winner player 2 height in inches |
| w_p2_country | Winner player 2 country |
| w_rank | Winner team rank |
| l_player1 | Losing player 1 name |
| l_p1_age | Losing player 1 age |
| l_p1_hgt | Losing player 1 height in inches |
| l_p1_country | Losing player 1 country |
| l_player2 | Losing player 2 name |
| l_p2_age | Losing player 2 age |
| l_p2_hgt | Losing player 2 height in inches |
| l_p2_country | Losing player 2 country |
| w_rank | Losing team rank |
| score | Match score separated by a dash and matches separated by a comma, eg 21 points to 12 points is 21-12 |
| num_total | Number of matches host in every country each year |
| num_winner | Number of matches with winners from the host country |
| win_rate | Home winning rate |
| num_rank | Number of matches with lower ranking team defeat higher one |
| rank_prop | Proportion of matches with lower ranking team defeat higher one |
The original data is sourced from: Vagner, A. (2020, July 20). BigTimeStats/beach-volleyball. Retrieved August 22, 2020, from https://github.com/BigTimeStats/beach-volleyball
To load the data set, we had to use a GitHub repository that had the data set. The name of this repository is “Tidy Tuesday”. The data set was sourced from this repository: Mock, J. (2020, May 19). rfordatasciene/tidytuesday. Retrieved August 22, 2020, from https://github.com/rfordatascience/tidytuesday/blob/master/data/2020/2020-05-19/readme.md
For both the AVP and FIVB tournaments, a team consists of 2 players. Each player in the team either comes from the same country or they can come from different countries. Thus, in this section, our analysis focuses on finding the countries that had the most number of winning teams. This will help us find the countries that had the most winning players.
In order to find our answer to this question, we first did some data wrangling to get the data set up for analysis. Then we followed the steps outlined below:
Figure 3.1: Top 20 countries with the most winning teams
Figure 3.2: Top 20 countries with the most winning teams in FIVB Circuit
Figure 3.1 shows the top 20 countries with the most number of winning teams. We can see that the United States was the most dominating country with a total of 4200 winning teams. This means that at minimum 8400 players came from the United States and won. In distant second place, Brazil had 258 winning teams, and so 516 Brazilian players won matches where both players in the team came from Brazil. In a close third place, Germany triumphed with 200 winning teams comprising of 400 players. The remaining 17 teams in this plot ranged from having 166 winning teams to 45 winning teams.
The clear winner here is United States and we can conclude that majority of the winning players in the AVP and FIVB tournaments hail from the United States.
But if we consider Figure 3.2 we can notice a different picture. FIVB circuit is the world championships where countries play against each other instead of players centric AVP. Looking at this plot we can see that in world championships teams from countries like Brazil give strong competition to U.S.
We decided to dig further into United States. Although there were 4200 teams where both players in each team came from the United States, there were instances were 1 player came from the United States and another player came from a different country. This following section takes a look at the different countries that partnered with the United States.
In order to find the different countries that partnered with the United States, we followed the steps outlined below:
This gave us a list of all the different country combinations where either player 1 or player 2 came from the United States and the other non-USA player’s country.
| Player_1_country | Player_2_country | Number_of_teams |
|---|---|---|
| United States | United States | 4200 |
| United States | Brazil | 44 |
| Poland | United States | 34 |
| Canada | United States | 25 |
| Brazil | United States | 24 |
| United States | Canada | 23 |
| United States | Poland | 20 |
| Virgin Islands | United States | 19 |
| United States | Australia | 18 |
| United States | England | 16 |
| United States | Puerto Rico | 15 |
| United States | Virgin Islands | 14 |
| Puerto Rico | United States | 13 |
| Greece | United States | 12 |
| United States | Israel | 11 |
| Italy | United States | 10 |
| United States | France | 10 |
| Philippines | United States | 9 |
| Costa Rica | United States | 8 |
| England | United States | 8 |
Table 3.1 shows 20 different country combinations, which is only a subset of the different countries that partnered with the United States. In total there were 66 different combinations.
Apart from both players coming from the United States, 44 different teams had player 1 come from the United States and player 2 come from Brazil. 34 teams had player 1 come from Poland and player 2 come from the United States.
From looking at the rest of the table, we can see just how popular the United States is as a competing country in volleyball tournaments. It not only registers in tournaments where both players come from the United States, but it also registers where only 1 player in the team comes from the United States and partners with a player from a different country.
N.B. For the method used to complete this analysis, please refer to the commentary included within the code chunks.
The average age for male winning players 1 and 2 are Mean :29.37 and Mean :29.29 respectively. The average age for male losing players 1 and 2, on the other hand, are Mean :29.05 and Mean :28.92 respectively. There is no obvious bias to winning and losing due to age - as the average age for losers and winners is about the same.
This might tell us something, however, about the average age of participation in professional male volleyball. If we plot every age of, for instance, male winning player 1 (Figure 3.3) and male losing player 2 (Figure 3.4) as examples, we see that the most commonly occurring ages are in the late 20s (28-29 year of age). Therefore, it is reasonable to infer that male volleyball players - due to the high levels of participation at those ages – hit their peak in their late 20s.
Now, let’s consider women’s volleyball. The average age for female winning players 1 and 2 are Mean :27.96 and Mean :29.29 respectively. The average age for female losing players 1 and 2 are Mean :29.05 and Mean :28.92 respectively. As was the case with the male game, age does not seem to strongly influence winning. However, it is interesting to note that their is a slight difference in average age of winning and losing players between the genders. If we take a look at the average age of winning player 2 in Figure 3.5, we can see that the average age of winning player 2 is less for females than males. Similarly, if we consider the average age of losing player 1 in Figure 3.6, we can see that the average age is also less for females than it is for males.
Figure 3.3: Ages of Male Winning Player 1
Figure 3.4: Ages of Male Losing Player 2
Figure 3.5: Ages of Winning Player 2 by gender
Figure 3.6: Ages of Losing Player 1 by gender
N.B. For the method used to complete this analysis, please refer to the commentary included within the code chunks.
The average height for female winning players 1 and 2 are Mean :70.91 and Mean :70.85 inches respectively. The average height for female losing players 1 and 2 are Mean :70.62 and Mean :70.72 inches respectively. Although the average height for the losing players is less than the height of winning players, it is not a huge difference.
The average height for male winning players 1 and 2 are Mean :76.28 and Mean :76.39 inches respectively, compared to the height for losing players 1 and 2 of Mean :75.98 and Mean :76.15 inches respectively. Consider Figures 3.7 and 3.8, which display the difference in heights between male winning and losing players 1 (Fig. 3.7) and male winning and losing player 2 (Fig. 3.8). In both situations, the means in difference in height are pretty evenly centred around 0. so we probably can’t say height difference effects winning a volleyball game. We can however say that male volleyball participants are generally taller than female volleyball participants although through common sense we know this phenomenon is not unique to just volleyball.
Figure 3.7: Difference in Heights of Male Player 1
Figure 3.8: Difference in Heights of Male Player 2
In team sports, the term home advantage describes the benefit that the home team is said to gain over the visiting team. This is because the home team will be more adaptable to the weather, temperature and other natural factors in the competition area. Additionally, there will be no jet lag problem, and there will also be a sense of security on the psychological level. Therefore, home advantage is a frequently mentioned topic in sports competitions. This time is no exception, we will also be curious whether the winning team of beach volleyball will have home advantage, which will be analyzed as followed.
Firstly, since the host country and contestant’s country in AVP competition is almost the United States, it is meaningless to discuss this issue, so I only choose the data of FVIB competition as the object. Then let’s see the home winning rate regardless of gender. I select the observations that has country where tournament played equal the country where winner is from. And then compute the number of these matches and save it as variable “num_winner”. After that, I compute the total number of matched host in every country each year and save it as variable “num_total”. Next, I join these two tables together to calculate the winning rate. Finally, I divide “num_winner” by “num_total” to get the winning rate regardless gender.
After getting the results, I make a bar plot to show this with a descending order.
Looking into Figure 3.9, it can be observed that in all the eight years, although team of Brazil has the highest winning rate at 32.1256039%, all the winning rate at home is less than fifty percentage, that is to say, the winning rate at home is not higher than that at away, which shows that the home advantage is not obvious in FVIB competition.
Figure 3.9: Home winning rate for all teams in FIVB
Although the home court advantage is not obvious for the winning team in general, is there any difference between the winning teams of different genders?
Then we comes to women’s team. On the basis of the previous part of the method, I added gender screening with screening the teams only for female gender, and calculated the home winning rate, then displayed the results in Figure 3.10. It can be seen that with Brazil having the highest rate at 34.2182891%, all of the teams don’t have rates over fifty percent, quite same as the general situation. That indicates that home advantage is still not obvious in women’s team.
Figure 3.10: Home winning rate for Woman
Using the same method of screening women’s teams, the teams whose gender is only male are selected and the winning rate at home is calculated after that. The results are shown in Figure 3.11. It is quite interesting that the home advantage is also not obvious in men, even if the highest rate is reached 30.1044634% by Brazil.
Figure 3.11: Home winning rate for Man
General speaking, home advantage is not tenable for the winning team in FVIB tournament, regardless of gender. However, if we look further, we can find that there are both some gaps in graphs of men and women. For example, there is no male team in Korea having a home winning, and there is no female team in Oman gaining home winning either, which may indicate that the strength of men’s or women’s beach volleyball in these countries is not enough or is not attached much attention to. But in any case, Brazil has the most home winning rate, although it does not have the most number of winning teams.
Through the analysis, we can know that the winning team may be a strong team, but is there any situation that the low ranking team defeats the higher one? First, I focus on FVIB tournament, and filter the matches in which the low ranking team defeated the higher one for women. And then compute the number of these matches and save it as variable “num_rank” . After that, I compute the total number of matched host in every country each year and save it as variable “num_total”. Next, I join these two tables together to calculate the proportion of teams with low ranking but defeating the higher one. Finally, I divide “num_rank” by “num_total” to get the results.Second, I use the same method as above to compute the rate for men.
In Figure 3.12, for female,it can be seen that tournament in Liechtenstein has the most proportion of team defeating teams higher ranking them at about 67.5%, and the lowest tournament is in Morocco at 37.254902%. Most of the tournaments have over half teams defeating the higher ranked teams.
Figure 3.12: Low ranking team beat higher ranking team(Woman FVIB)
Figure 3.13 shows the results of men. The tournament in Canada had most proportion, about 67.7419355% teams defeating higher ranked one. The only three that was not over fifty percent are Argentina ,Rwandaand Puerto Rico with proportion at 48.9130435% , 48.2758621 and 47.3684211%. Similar to women, most tournament for men had over half team defeating higher ranked one.
However, we could also recognize that this proportion of women is greater than that of men for most countries, which indicates that the overall strength of the women’s team is stronger than that of the men’s team.
Figure 3.13: Low ranking team beat higher ranking team(Man FVIB)
Then, it comes to the AVP tournament. I use the same method applied in the analysis of FVIB. But in order to display the women and men rate in one plot, I manually create a tibble that only contains the gender and the rate value. As the host country in AVP is all America, I ignore the country variable. I also draw a plot to represent the results.
In Figure 3.14, the bar chart on the left side is the rate of men with the right-side one showing the rate of women team. It can be observed that the rate of men is about 50.25072%, and the rate of women is around 51.14613%. We can see that in the AVP competition, the gender difference is not obvious. Similarly, more than half of the teams can beat the higher ranked teams.
Figure 3.14: Low ranking team beat higher ranking team (AVP)
Generally speaking, the situation that the lower ranked teams beat the higher ranked teams accounts for more than half of the total in both FVIB and AVP tournaments. Therefore, we can say that it is not uncommon for low ranking teams to beat high ranked ones in beach volleyball. It also indirectly indicates that ranking in beach volleyball competition may not fully reflect the strength and winning rate of a team.
| player1 | player2 | Count |
|---|---|---|
| Juliana Felisberta | Larissa Franca | 617 |
| Carolina Salgado | Maria Clara Salgado | 577 |
| Emanuel Rego | Ricardo Santos | 562 |
| Adrian Gavira | Pablo Herrera | 529 |
| Ilka Semmler | Katrin Holtwick | 495 |
| Elsa Baquerizo | Liliana Fernandez | 469 |
| Emilia Nystrom | Erika Nystrom | 460 |
| Doris Schwaiger | Stefanie Schwaiger | 458 |
| Kerri Walsh Jennings | Misty May-Treanor | 446 |
| Chen Xue | Xi Zhang | 434 |
Table 3.2 shows top 10 different combinations of players that have teamed up for the greatest number of matches in FIVB circuit, which is only a subset of the total combinations of players. In total there were 5,613 unique combinations. Juliana Felisberta and Larissa Franca partnered up for the most number of times across FIVB tournaments followed by Carolina Salgado and Maria Clara Salgado.
| player1 | player2 | Count |
|---|---|---|
| Annett Davis | Jenny Johnson Jordan | 500 |
| Katie Jameson | Tracy Jones | 422 |
| Kerri Walsh Jennings | Misty May-Treanor | 400 |
| Casey Jennings | Matt Fuerbringer | 380 |
| Phil Dalhausser | Todd Rogers | 362 |
| Jake Gibb | Sean Rosenthal | 350 |
| Michelle Williams | Suzanne Barnes | 289 |
| April Ross | Jennifer Kessy | 273 |
| Nick Lucena | Phil Dalhausser | 235 |
| Elaine Youngs | Nicole Branagh | 232 |
Table 3.3 shows top 10 different combinations of players that have teamed up for the greatest number of matches in AVP circuit, which is only a subset of the total combinations of players. In total there were 7,872 unique combinations. Annett Davis and Jenny Johnson Jordan partnered up for the most number of times across AVP tournaments followed by Katie Jameson and Tracy Jones.
| player1 | player2 | Count |
|---|---|---|
| Juliana Felisberta | Larissa Franca | 520 |
| Emanuel Rego | Ricardo Santos | 446 |
| Kerri Walsh Jennings | Misty May-Treanor | 398 |
| Carolina Salgado | Maria Clara Salgado | 364 |
| Adrian Gavira | Pablo Herrera | 346 |
| Adriana Behar | Shelda Bede | 339 |
| Chen Xue | Xi Zhang | 334 |
| April Ross | Jennifer Kessy | 301 |
| Ilka Semmler | Katrin Holtwick | 296 |
| Aleksandrs Samoilovs | Janis Smedins | 287 |
Table 3.4 shows top 10 combinations of the players that are most successful in the AVP volleyball circuit. Juliana Felisberta and Larissa Franca is the most successful team across FIVB organised tournaments followed by Emanuel Rego and Ricardo Santos.
| player1 | player2 | Count |
|---|---|---|
| Kerri Walsh Jennings | Misty May-Treanor | 384 |
| Annett Davis | Jenny Johnson Jordan | 336 |
| Phil Dalhausser | Todd Rogers | 323 |
| Casey Jennings | Matt Fuerbringer | 253 |
| Jake Gibb | Sean Rosenthal | 246 |
| Katie Jameson | Tracy Jones | 221 |
| April Ross | Jennifer Kessy | 208 |
| Elaine Youngs | Nicole Branagh | 188 |
| Nick Lucena | Phil Dalhausser | 166 |
| Michelle Williams | Suzanne Barnes | 149 |
Table 3.5 shows top 10 combinations of the players that are most successful in the AVP volleyball circuit. Kerri Walsh Jennings and Misty May-Treanor is the most successful team across AVP organised tournaments followed by Annett Davis and Jenny Johnson Jordan.
| player | Matches_Won |
|---|---|
| Juliana Felisberta | 649 |
| Emanuel Rego | 571 |
| Alison Cerutti | 502 |
| April Ross | 481 |
| Carolina Salgado | 471 |
| Chen Xue | 462 |
| Kerri Walsh Jennings | 454 |
| Aleksandrs Samoilovs | 448 |
| Benjamin Insfran | 394 |
| Adrian Gavira | 381 |
Table 3.6 shows top 10 most successful players in the FIVB volleyball circuit. Juliana Felisberta leads with 649 combined wins so far followed by Emanuel Rego and 571.
Figure 3.15: Top 5 successful players growth in terms of win overtime in FIVB
Figure 3.15 shows the growth of top 5 successful players as identified in table 3.6. It can be noticed that Emanuel Rego had been a consistent player over the years participating in almost every tournament organised by FIVB. Both Juliana Felisberta and Emanuel Rego shows a positive ratio between their win and total matches played overtime.
| player | Matches_Won |
|---|---|
| Elaine Youngs | 448 |
| Kerri Walsh Jennings | 426 |
| Jake Gibb | 393 |
| Phil Dalhausser | 364 |
| Annett Davis | 351 |
| April Ross | 347 |
| Casey Jennings | 320 |
| Nick Lucena | 293 |
| Angie Akers | 288 |
| Casey Patterson | 267 |
Table 3.7 shows top 10 most successful players in the AVP volleyball circuit. Elaine Youngs leads with 448 combined wins so far followed by Kerri Walsh Jennings and 426.
Figure 3.16: Top 5 successful players growth in terms of win overtime in AVP
Figure 3.16 shows the growth of top 5 successful players as identified in table 3.7. It can be noticed that AVP has some rather different output as compared to FIVB. Elaine Youngs although has the highest number of wins but she has not played any matches in AVP tournaments after that. The most strong player has to be Kerri Walsh Jennings with a strong win rate compared to matches played.
After our analysis, we have concluded that a typical winning male volleyball team most likely has both players originating from the United States, with player one having an average age of Mean :29.37 and an average height of Mean :76.28 inches with player two having an average age of Mean :29.29 and an average height of Mean :76.39 inches.
In addition, a typical winning female volleyball team most likely has both players originating from the United States, with player one having an average age of Mean :27.96 and an average height of Mean :70.91 inches with player two having an average age of Mean :29.29 and an average height of Mean :76.39 inches.
As for the home advantage, although team of Brazil has the highest winning rate at NA%, all the winning rate at home is less than fifty percentage, that is to say, the winning rate at home is not higher than that at away, which shows that the home advantage is not obvious in FVIB competition regardless of gender. But there does exist some gaps between male and female.
When it comes to the lower ranking team defeat the higher ranking one, first in FVIB circuit, it can be concluded that the most proportions of this for female and male are 67.5% by Liechtenstein and 67.7419355% by Canada respectively. Then in AVP circuit,the most proportions of this for female and male are `51.14613%% and 50.25072%% all by United States. So, it is not uncommon for low ranking teams to beat high ranked ones in beach volleyball. It also indirectly indicates that ranking in beach volleyball competition may not fully reflect the strength and winning rate of a team. Also, gender gap is not obvious on this issue.
Also, when we look at the players and how they have teamed up, Juliana Felisberta and Larissa Franca partnered up for the most number of times across FIVB followed by Carolina Salgado and Maria Clara Salgado and Annett Davis and Jenny Johnson Jordan partnered up for the most number of times across AVP followed by Carolina Salgado and Maria Clara Salgado.
Among the player combinations present in both AVP and FIVB, Juliana Felisberta has been the most successful player in FIVB with 649 wins and Elaine Youngs has been the most successful player in AVP with 448.
Thanks for the contributors of these packages:
ggpplot2 (Wickham 2016)
tidyverse (Wickham et al. 2019)
kableExtra (Zhu 2019)
bookdown (Xie 2020)
gridExtra (Auguie 2017)
plotly (Sievert 2020)
lubridate (Grolemund and Wickham 2011)
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Grolemund, Garrett, and Hadley Wickham. 2011. “Dates and Times Made Easy with lubridate.” Journal of Statistical Software 40 (3): 1–25. http://www.jstatsoft.org/v40/i03/.
Sievert, Carson. 2020. Interactive Web-Based Data Visualization with R, Plotly, and Shiny. Chapman; Hall/CRC. https://plotly-r.com.
Wickham, Hadley. 2016. Ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. https://ggplot2.tidyverse.org.
Wickham, Hadley, Mara Averick, Jennifer Bryan, Winston Chang, Lucy D’Agostino McGowan, Romain François, Garrett Grolemund, et al. 2019. “Welcome to the tidyverse.” Journal of Open Source Software 4 (43): 1686. https://doi.org/10.21105/joss.01686.
Xie, Yihui. 2020. Bookdown: Authoring Books and Technical Documents with R Markdown. https://github.com/rstudio/bookdown.
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